Radar System with Sparse Primary Array and Dense Auxiliary Array

ABSTRACT

This document describes techniques and components of a radar system with a sparse primary array and a dense auxiliary array. Even with fewer antenna elements than a traditional radar system, an example radar system has a comparable angular resolution at a lower cost, lower complexity level, and without aliasing. The radar system includes a processor and antenna arrays that can receive electromagnetic energy reflected by one or more objects. The antenna arrays include a primary subarray and an auxiliary subarray. The auxiliary subarray includes multiple antenna elements with a smaller spacing than the antenna elements of the primary subarray. The processor can determine, using the received electromagnetic energy, first and second potential angles associated with the one or more objects. The processor then associates, using the first and second potential angles, respective angles associated with each of the one or more objects.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.17/153,788, filed Jan. 20, 2021, which claims the benefit under 35U.S.C. 119(e) of U.S. Provisional Application No. 63/091,193, filed Oct.13, 2020, the disclosures of which are hereby incorporated by referencein their entireties herein.

BACKGROUND

Radar systems use antennas to transmit and receive electromagnetic (EM)signals for detecting and tracking objects. In automotive applications,radar antennas can include a linear array of elements to measure azimuthor elevation angles associated with nearby objects. The angularresolution of such a radar system is generally proportional to theaperture size of the linear array. A large aperture with a linear arraycan require many antenna elements, which increases cost, or largerspacing among the antenna elements, which may introduce aliasing inangles (e.g., grating lobes). It is desirable to maintain the angularresolution of radar systems without significant cost increases orintroducing aliasing.

SUMMARY

This document describes techniques and components of a radar system witha sparse primary array and a dense auxiliary array. Even with fewerantenna elements than a traditional radar system, an example radarsystem has a comparable angular resolution but at a lower cost, lowercomplexity level, and without aliasing. The radar system includes aprocessor and an antenna array that can receive electromagnetic energyreflected by one or more objects. The antenna array includes a primarysubarray and an auxiliary subarray. The auxiliary subarray includesmultiple antenna elements with a smaller spacing than the antennaelements of the primary subarray. The processor can determine, using thereceived electromagnetic energy, first and second potential anglesassociated with the one or more objects. The processor then associates,using the first and second potential angles, respective anglesassociated with each of the one or more objects.

This document also describes methods performed by the above-summarizedsystem and other configurations of the radar system set forth herein, aswell as means for performing these methods.

This Summary introduces simplified concepts related to a radar systemwith a sparse primary array and a dense auxiliary array, furtherdescribed in the Detailed Description and Drawings. This Summary is notintended to identify essential features of the claimed subject matter,nor is it intended for use in determining the scope of the claimedsubject matter.

BRIEF DESCRIPTION OF THE DRAWINGS

The details of one or more aspects of a radar system with a sparseprimary array and a dense auxiliary array are described in this documentwith reference to the following figures. The same numbers are often usedthroughout the drawings to reference like features and components:

FIG. 1 illustrates an example environment in which a radar system with asparse primary array and a dense auxiliary array can be implemented;

FIGS. 2A-2D illustrate example antenna arrays with a sparse primarylinear array and a dense auxiliary linear array;

FIG. 3 illustrates an example antenna array with a sparse primarytwo-dimensional array and a dense auxiliary two-dimensional array;

FIG. 4 illustrates an example conceptual diagram of a radar system witha sparse primary array and a dense auxiliary array;

FIG. 5-6 illustrate example conceptual diagrams of an angle-findingmodule to determine angles of nearby objects based on EM energy receivedby a sparse primary array and a dense auxiliary array; and

FIG. 7 illustrates a flow diagram of an example method of a radar systemwith a sparse primary array and a dense auxiliary array.

DETAILED DESCRIPTION

Overview

Radar systems are an essential sensing technology that vehicle systemsrely on to acquire information about the surrounding environment. Radarsystems generally include at least two antennas to transmit and receiveEM radiation. Some radar systems include at least one receive antennawith one or more linear arrays of antenna elements to measure theazimuth and/or elevation angles associated with objects. A largeaperture in the azimuth or elevation direction can increase the numberof antenna elements and the cost of the radar system.

Some radar systems include a receive antenna with one or more uniformlinear arrays of antenna elements. A uniform linear array can provide alarge aperture to achieve smaller beam widths and improved angularresolution. The Nyquist-Shannon sampling theorem can be used duringdesign to limit the spacing of the antenna elements in linear arrays andto avoid introducing aliasing effects within the field-of-view. Due tothese restrictions, larger apertures generally result in a greaternumber of antenna elements. Radar systems in automotive applications,however, often have a small number of antenna channels available, whichresults in low angular resolution.

Other radar systems include a receive antenna with a sparse array ofantenna elements. In such radar systems, the sparse array can have thesame aperture as a dense array but removes antenna elements to reducethe number of antenna elements. The greater the number of removedantenna elements in the sparse array, the greater the number ofpotentially aliased angles. Although such radar systems generallyinclude fewer antenna elements than dense arrays, the angle-findingprocessing for these systems is too complicated for many applications,including automotive applications. In particular, such radar systemsrequire complex processing methods or multiple data snapshots tosuppress aliasing and detect small objects. Because these processingmethods generally cannot be processed in real time and automotive radarsystems generate a single snapshot as the vehicle moves, these methodsare generally not available for automotive applications.

In contrast, this document describes techniques and systems to provide areceive antenna array with a sparse primary subarray and a denseauxiliary subarray. The primary subarray includes multiple first antennaelements, and the auxiliary subarray includes multiple second antennaelements that have a smaller spacing than the first antenna elements.The sparse primary subarray provides the radar system with improvedangular resolution. The dense auxiliary subarray provides angularde-aliasing. In this way, the described systems and techniques canreduce the number of antenna elements, cost, and computationalcomplexity.

The radar system determines, using EM energy received at the primarysubarray and the auxiliary subarray, first potential angles and secondpotential angles, respectively, associated with one or more objects. Theradar system can then associate the first and second potential angleswith respective angles associated with each of the one or more objects.In this way, the computational complexity for the described radar systemto associate the first potential angles and second potential angles torespective objects is similar to the computational complexity for aconventional radar system with linear subarrays. Radar systems can applythe described angle-finding techniques to various configurations of asparse primary array and a dense auxiliary array.

This is just one example of the described techniques and systems of aradar antenna array with a sparse primary array and a dense auxiliaryarray. This document describes other examples and implementations.

Operating Environment

FIG. 1 illustrates an example environment 100 in which a radar system102 with a sparse primary array and a dense auxiliary array can beimplemented. In the depicted environment 100, the radar system 102 ismounted to, or integrated within, a vehicle 104. The radar system 102can detect one or more objects 120 that are in proximity to the vehicle104.

Although illustrated as a car, the vehicle 104 can represent other typesof motorized vehicles (e.g., a motorcycle, a bus, a tractor, asemi-trailer truck), non-motorized vehicles (e.g., a bicycle), railedvehicles (e.g., a train), watercraft (e.g., a boat), aircraft (e.g., anairplane), or spacecraft (e.g., satellite). In general, manufacturerscan mount the radar system 102 to any moving platform, including movingmachinery or robotic equipment.

In the depicted implementation, the radar system 102 is mounted on thefront of the vehicle 104 and illuminates the object 120. The radarsystem 102 can detect the object 120 from any exterior surface of thevehicle 104. For example, vehicle manufacturers can integrate the radarsystem 102 into a bumper, side mirror, headlights, rear lights, or anyother interior or exterior location where the object 120 requiresdetection. In some cases, the vehicle 104 includes multiple radarsystems 102, such as a first radar system 102 and a second radar system102, that provide a larger instrument field-of-view. In general, vehiclemanufacturers can design the locations of one or more radar systems 102to provide a particular field-of-view that encompasses a region ofinterest. Example fields-of-view include a 360-degree field-of-view, oneor more 180-degree fields-of-view, one or more 90-degree fields-of-view,and so forth, which can overlap into a field-of-view of a particularsize.

The object 120 is composed of one or more materials that reflect radarsignals. Depending on the application, the object 120 can represent atarget of interest. In some cases, the object 120 can be a moving object(e.g., another vehicle) or a stationary object (e.g., a roadside sign).

The radar system 102 emits EM radiation by transmitting EM signals orwaveforms via antenna elements. In the environment 100, the radar system102 can detect and track the object 120 by transmitting and receivingone or more radar signals. For example, the radar system 102 cantransmit EM signals between 100 and 400 gigahertz (GHz), between 4 and100 GHz, or between approximately 70 and 80 GHz.

The radar system 102 can include a transmitter 106 and at least oneantenna 110 to transmit EM signals. The radar system 102 can alsoinclude a receiver 108 and the at least one antenna 110 to receivereflected versions of the EM signals. The transmitter 106 includes oneor more components for emitting the EM signals. The receiver 108includes one or more components for detecting the reflected EM signals.Manufacturers can incorporate the transmitter 106 and the receiver 108together on the same integrated circuit (e.g., configured as atransceiver) or separately on different integrated circuits.

The radar system 102 also includes one or more processors 112 (e.g., anenergy processing unit) and computer-readable storage media (CRM) 114.The processor 112 can be a microprocessor or a system-on-chip. Theprocessor 112 can execute instructions stored in the CRM 114. Forexample, the processor 112 can process EM energy received by the antenna110 and determine, using an angle-finding module 116, a location of theobject 120 relative to the radar system 102. The processor 112 can alsogenerate radar data for at least one automotive system. For example, theprocessor 112 can control, based on processed EM energy from the antenna110, an autonomous or semi-autonomous driving system of the vehicle 104.

The angle-finding module 116 obtains EM energy received by the antenna110 and determines azimuth angles and/or elevation angles associatedwith the object 120. The radar system 102 can implement theangle-finding module 116 as instructions in the CRM 114, hardware,software, or a combination thereof that is executed by the processor112.

The radar system 102 can determine a distance to the object 120 based onthe time it takes for the EM signals to travel from the radar system 102to the object 120 and from the object 120 back to the radar system 102.The radar system 102 can also determine, using the angle-finding module116, a location of the object 120 in terms of an azimuth angle 126and/or an elevation angle (not illustrated in FIG. 1 ) based on thedirection of a maximum-amplitude echo signal received by the radarsystem 102.

As an example, FIG. 1 illustrates the vehicle 104 traveling on a road118. The radar system 102 detects the object 120 in front of the vehicle104. The radar system 102 can define a coordinate system with an x-axis122 (e.g., in a forward direction along the road 118) and a y-axis 124(e.g., perpendicular to the x-axis 122 and along a surface of the road118). The radar system 102 can locate the object 120 in terms of theazimuth angle 126 and/or the elevation angle. The azimuth angle 126 canrepresent a horizontal angle from the x-axis 122 to the object 120. Theelevation angle can represent a vertical angle from the surface of theroad 118 (e.g., a plane defined by the x-axis 122 and the y-axis 124) tothe object 120.

The vehicle 104 can also include at least one automotive system thatrelies on data from the radar system 102, such as a driver-assistancesystem, an autonomous-driving system, or a semi-autonomous-drivingsystem. The radar system 102 can include an interface to an automotivesystem that relies on the data. For example, the processor 112 outputs,via the interface, a signal based on EM energy received by the antenna110.

Generally, the automotive systems use radar data provided by the radarsystem 102 to perform a function. For example, the driver-assistancesystem can provide blind-spot monitoring and generate an alert thatindicates a potential collision with the object 120 that is detected bythe radar system 102. The radar data from the radar system 102 indicateswhen it is safe or unsafe to change lanes in such an implementation. Theautonomous-driving system may move the vehicle 104 to a particularlocation on the road 118 while avoiding collisions with the object 120detected by the radar system 102. The radar data provided by the radarsystem 102 can provide information about a distance to and the locationof the object 120 to enable the autonomous-driving system to performemergency braking, perform a lane change, or adjust the speed of thevehicle 104.

FIGS. 2A through 2D illustrate example antenna arrays 200, in particularantenna arrays 200-1, 200-2, 200-3, and 200-4, with a sparse primarylinear array and a dense auxiliary linear array. The antenna arrays 200are examples of the antenna 110 of the radar system 102 in FIG. 1 , withsimilar components.

In the depicted implementations, the antenna arrays 200 include a sparseuniform linear array (ULA) 204 as the primary linear array and a denseULA 206 as the auxiliary linear array on a printed circuit board (PCB)202. In some implementations, the antenna array 200 can includeadditional dense ULAs (e.g., second dense ULA 220), as illustrated inFIG. 2D. In operation, the antenna arrays 200 can receive EM energyreflected by one or more objects 120.

The sparse ULA 204 and the dense ULA 206 are positioned in an azimuthdirection in the depicted implementations. The sparse ULA 204 and thedense ULA 206 may be positioned in an elevation direction in otherimplementations, depending on the application or intended use. Theantenna array 200 can include sparse ULAs 204 and dense ULAs 206 thatare positioned in both an azimuth direction and an elevation direction,in yet other implementations.

The sparse ULA 204 and the dense ULA 206 can be arranged in variouspositions or orientations. For example, the dense ULA 206 can be offsetfrom the sparse ULA 204 in an azimuth direction, as illustrated in FIG.2A; in an elevation direction, as illustrated in FIG. 2D; or in both anazimuth direction and an elevation direction, as illustrated in FIG. 2B.The sparse ULA 204 and the dense ULA 206 can overlap, as illustrated inFIG. 2C, with some overlapping antenna elements 214 (e.g., overlappingelement 218-1, overlapping element 218-2) shared by both the sparse ULA204 and the dense ULA 206. The antenna elements 208 of the sparse ULA204 and the dense ULA 206 may generally be positioned at differentrelative locations as long as the far-field planar incident waveassumption is satisfied.

The sparse ULA 204 and the dense ULA 206 can include physical, digital,or synthetic arrays of receiver antenna elements. The sparse ULA 204 andthe dense ULA 206 can also form various phased-array radar systems,including a multiple-input multiple-output (MIMO) radar. MIMO radarsystems generally employ digital receiver arrays distributed across anaperture, with antenna elements 208 generally closely located to obtaina better spatial resolution, Doppler resolution, and dynamic range.

In some cases, the antenna elements 208 of the sparse ULA 204 and thedense ULA 206 can be arranged in other configurations and positions. Forexample, the antenna array 200 can include the second dense ULA 220, asillustrated in FIG. 2D, or additional dense ULAs. In otherimplementations, the sparse ULA 204 and the dense ULA 206 can bereplaced with non-uniform linear arrays and utilize interpolation andother algorithms than those disclosed below to determine the angles ofthe objects 120. The sparse ULA 204 and the dense ULA 206 may bearranged to optimize range or range-rate detections.

The sparse ULA 204, the dense ULA 206, and the second dense ULA 220include multiple antenna elements 208. The sparse ULA 204 can include Mantenna elements 208. The dense ULA 206 can include N antenna elements208, where N is generally equal to or less than M. In automotiveapplications, the number of antenna elements 208 in the dense ULA 206 isgenerally greater than an anticipated maximum number of objects 120 tobe detected by the radar system 102.

In the depicted implementations, the sparse ULA 204 includes nineantenna elements 208, the dense ULA 206 includes six antenna elements208, and the second dense ULA 220 includes six antenna elements 208. Theantenna elements 208 in the sparse ULA 204 are separated by a sparsespacing 210, d_(S). Similarly, the antenna elements 208 in the dense ULA206 are separated by a dense spacing 212, d_(D). The sparse spacing 210is larger than the dense spacing 212 (e.g., d_(S)>d_(D)). The sparse ULA204 has a sparse aperture 214, As, and the dense ULA 206 has a denseaperture 216, A_(D). The dense aperture 216 is generally smaller thanthe sparse aperture 214.

In some implementations, the ratio of the sparse spacing 210 to thedense spacing 212 is equal to an integer (e.g., K=d_(S)/d_(D)), where Kis an integer. In other implementations, the ratio of the sparse spacing210 to the dense spacing 212 is equal to a factor of two (e.g.,2^(n)=d_(S)/d_(D)), where n is a positive integer (e.g., n=1, 2, 3, 4,5, etc.).

The angle coverage (e.g., field-of-view), θ, of the dense ULA 206 can becalculated using the dense spacing 212, d_(D), as shown in Equation 1:

$\begin{matrix}{{{- {\sin^{- 1}\left( \frac{\lambda}{2d_{D}} \right)}} \leq \theta \leq {\sin^{- 1}\left( \frac{\lambda}{2d_{D}} \right)}},} & (1)\end{matrix}$

where λ is the wavelength of the EM energy transmitted by the dense ULA206. Table 1 below lists the angle coverage for the dense ULA 206 as afunction of the dense spacing 212 and wavelength.

TABLE 1 Dense Distance 212 Angle Coverage 0.5λ ±90° 1λ ±30° 1.5λ ±19.47°2λ ±14.48° 2.5λ ±11.540° 3λ  ±9.59° 3.5λ  ±8.21° 4λ  ±7.18°As a result, the desired angle coverage can be used to define or set thevalue of the dense spacing 212.

After selecting the dense spacing 212, the sparse spacing 210 can beselected based on the value of K, which represents the number of aliasedangles from the sparse ULA 204. If the value of K is too large, thepossibility of inaccurate de-aliasing can be high. In general, the valueof K, which represents the ratio of the sparse spacing 210 to the densespacing 212, should be less than 10.

The sparse ULA 204, the dense ULA 206, and the second dense ULA 220 canbe planar arrays that provide high gain and low loss. Planar arrays arewell-suited for vehicle integration due to their small size. Forexample, the antenna elements 208 can be slots etched or otherwiseformed in a plating material of one surface of the PCB 202 for asubstrate-integrated waveguide (SIW) antenna. The antenna elements 208can also be part of an aperture antenna, a microstrip antenna, or adipole antenna. For example, the sparse ULA 204, the dense ULA 206, andthe second dense ULA 220 can include subarrays of patch elements (e.g.,microstrip patch antenna subarrays) or dipole elements. The sparse ULA204, the dense ULA 206, and the second dense ULA 220 can be syntheticaperture arrays in other implementations.

FIG. 3 illustrates an example antenna array 300 with a sparsetwo-dimensional (2D) subarray 302 and a dense auxiliary 2D subarray 304.The antenna array 300 is an example of the antenna 110 of the radarsystem 102 in FIG. 1 , with similar components. In operation, theantenna array 300 can receive EM energy reflected by one or more objects120.

In the depicted implementation, the sparse 2D subarray 302 and the dense2D subarray 304 include antenna subarrays positioned in both the azimuthand elevation directions. The antenna elements of the dense 2D subarray304 overlap with those of the sparse 2D subarray 302. In otherimplementations, the dense 2D subarray 304 and the sparse 2D subarray302 may be arranged in various other positions. For example, the dense2D subarray 304 can partially overlap with the sparse 2D subarray 302 ornot overlap at all.

FIG. 4 illustrates an example conceptual diagram 400 of the radar system102 with a sparse linear array and a dense auxiliary linear array. Theradar system 102 of FIG. 4 can, for example, be the radar system 102 ofFIG. 1 . In the depicted implementation, the radar system 102 includesthe sparse ULA 204 and the dense ULA 206, which can be arranged invarious positions, including the arrangements illustrated in FIGS. 2Athrough 3 .

The sparse ULA 204 can generally achieve a high angular resolution andaccuracy. In some situations, the sparse ULA 204 can obtain betterangular resolution and accuracy than a dense array with 0.5λ spacingwith the same aperture. The angle estimates of the sparse ULA 204,however, can be aliased and appear on multiple angle regions. Incontrast, the dense ULA 206 can provide unaliased angle estimates withlower angular resolution and accuracy than the sparse ULA 204. Asdescribed below with respect to FIGS. 5 and 6 , the radar system 102 canuse the angle estimates from the dense ULA 206 to identify the correctangles for the objects 120. In this way, the described systems andtechniques combine the benefits of both the sparse ULA 204 and the denseULA 206.

At 404, the angle-finding module 116 obtains primary EM energy 402received by the sparse ULA 204 and determines potential primary angles406 associated with one or more objects 120. The potential primaryangles 406 include θ₁, θ₂, . . . , θ_(N) _(P) , where N_(P) representsthe number of objects detected by the sparse ULA 204.

At 410, the angle-finding module 116 obtains auxiliary EM energy 408received by the dense ULA 206 and determines potential auxiliary angles412 associated with the one or more objects 120. The potential auxiliaryangles 412 include φ₁, φ₂, . . . , φ_(N) _(A) , where N_(A) representsthe number of objects detected by the auxiliary ULA 206. Because thesparse ULA 204 and the dense ULA 206 have different apertures andresolutions, the number of potential primary objects, N_(P), can bedifferent than the number of potential auxiliary objects, N_(A). Forexample, the potential primary angles 406 can include two peaks (e.g.,potential objects) within a single angle interval for the potentialauxiliary angles 412.

The angle-finding module 116 can use various angle-finding functions todetermine the potential primary angles 406 and the potential auxiliaryangles 412 from the primary EM energy 402 and the auxiliary EM energy408, respectively. As non-limiting examples, the angle-finding module116 can use a pseudo-spectrum function, including an Estimation ofSignal Parameters via Rotational Invariance Technique (ESPRIT),Space-Alternating Generalized Expectation-maximization (SAGE),Delay-and-Sum (DS), Minimum Variance Distortionless Response (MVDR),and/or a Multiple Signal Classification (MUSIC) based-function, tocalculate the direction of arrival of the EM signals received by theprimary ULA 204 and the auxiliary ULA 206. The angle-finding module 116can determine the potential primary angles 406 and the potentialauxiliary angles 412 with relatively low processing complexity and cost.

At 414, the angle-finding module 116 determines, using the potentialprimary angles 406 and the potential auxiliary angles 412, the angleassociated with the objects 120. In particular, the angle-finding module116 determines the azimuth or elevation angle associated with each ofthe one or more objects 120. The association of the azimuth or elevationangles to the objects 120 is described in greater detail with respect toFIG. 5 .

FIG. 5 illustrates an example conceptual diagram 414 of theangle-finding module 116 to determine the angles associated with theobjects 120. The angle-finding module 116 of FIG. 5 can, for example, bethe angle-finding module 116 of FIGS. 1 through 4 . In particular, theangle-finding module 116 determines the angles associated with theobjects 120 using synthetic fast Fourier transform (FFT) spectrums fromthe primary EM energy 402 and the auxiliary EM energy 408. Because theprimary ULA 204 and the auxiliary ULA 206 are uniform linear arrays, theangle-finding module 116 can use FFT spectrums with a pre-defined window(e.g., a Chebyshev window) to suppress sidelobes.

At 502, the angle-finding module 116 generates FFT spectrum magnitudesfor the primary ULA 204 and the auxiliary ULA 206 using the primary EMenergy 402 and the auxiliary EM energy 408, respectively. For example,the angle-finding module 116 can generate the FFT spectrum for theprimary EM energy 402 and the auxiliary EM energy 408. The angle-findingmodule 116 can then generate an unfolded FFT spectrum for the primary EMenergy 402 and the auxiliary EM energy 408.

At 504, the angle-finding module 116 normalizes and aligns the FFTspectrums or the unfolded FFT spectrums for the sparse ULA 204 and thedense ULA 206. For example, the angle-finding module 116 can align bothFFT spectrums according to the detected potential primary angles 406 andthe potential auxiliary angles 412. The angle-finding module 116 canidentify the potential angles as the magnitude peaks in the FFTspectrums.

At 506, the angle-finding module 116 identifies auxiliary spectrumpeaks. For example, the angle-finding module 116 can analyze the FFTspectrum for the dense ULA 206 and identify spectrum peaks above apre-defined threshold T The angle-finding module 116 can also identifythe angle areas associated with the spectrum peaks. The angle areaassociated with a specific auxiliary ULA spectrum peak generally spansthe peak location neighborhood. The angle-finding module 116 can extendthis angle area to contain possible primary ULA spectrum peaks whileavoiding apparent false detections.

The pre-defined threshold T can be related to the signal-to-noise ratio(SNR) for the dense ULA 206 and/or the sidelobe level from a pre-definedwindow function applied in the FFT. In general, the higher the SNR ofthe dense ULA 206, the lower the pre-defined threshold T can be set. Thepre-defined threshold T generally cannot exceed the dynamic range of thedense ULA 206.

At 508, the angle-finding module 116 identifies primary spectrum peaks.For example, the angle-finding module 116 can analyze the FFT spectrumfor the sparse ULA 204 and identify spectrum peaks above the pre-definedthreshold T The angle-finding module 116 identifies the primary spectrumpeaks in angle areas associated with the auxiliary spectrum peaks.

At 510, the angle-finding module 116 filters out unqualified spectrumpeaks. For example, the angle-finding module 116 can evaluate theauxiliary spectrum and the primary spectrum at locations for the primaryspectrum peaks. The angle-finding module 116 can compare the magnitude,slope, or a combination thereof of the candidate peaks to removeunexpected peaks and reduce the computational burden of furtherprocessing. The angle-finding module 116 can also evaluate additionalaspects of the candidate peaks to remove unexpected peaks.

In some implementations, the angle-finding module 116 can perform anorthogonal matching pursuit (OMP) procedure to further process thespectrums at optional operation A. The output of the OMP procedure isprovided at operation B. The operation of the angle-finding module 116to perform the OMP procedure is described in greater detail with respectto FIG. 6 .

At 512, the angle-finding module 116 outputs object angles for thenearby objects 120. For example, the angle-finding module 116 can outputcontinuous angle values associated with the final peaks throughinterpolation. When the ratio of the sparse spacing 210 to the densespacing 212 is equal to a factor of two (e.g., 2^(n)=d_(S)/d_(D)), theangle-finding module 116 can efficiently implement the describedsynthetic FFT spectrum processing due to the length of the FFT being apower of two. For other spacing ratios, the angle-finding module 116 mayneed to use interpolation to align the grid points of the primaryspectrum and the auxiliary spectrum.

FIG. 6 illustrates additional operations of the conceptual diagram 414for the angle-finding module 116 to determine the angles associated withthe objects 120. The angle-finding module 116 determines the anglesassociated with the objects 120 using an OMP procedure. Because theangular resolution of the dense ULA 206 is worse than that of the sparseULA 204, unfolding errors can exist in the FFT spectrum. Theangle-finding module 116 can use the OMP procedure to resolve the objectangles in such cases.

At 602, the angle-finding module 116 can generate an angle dictionary byunfolding the potential primary angles 406. As discussed above, thepotential primary angles 406 include θ₁, θ₂, . . . , θ_(N) _(P) . Forexample, the angle-finding module 116 can unfold the primary angles 406θ₁, θ₂, . . . , θ_(N) _(P) to the unfolded angles θ_(1,1), θ_(2,1), . .. , θ_(N) _(p,1) , . . . , θ_(,1K), θ_(2,K), . . . , θ_(N) _(p,K) forthe K intervals.

At 604, the angle-finding module 116 can filter the unfolded angles fromthe auxiliary spectrum to reduce the list of potential primary angles406. For example, the angle-finding module 116 can filter the unfoldedangles θ_(1,1), θ_(2,1), . . . , θ_(N) _(p,1) , . . . , θ_(1,K),θ_(2,K), . . . , θ_(N) _(p,K) from the auxiliary spectrum with filterwindows. In this way, the angle-finding module 116 can reduce the listof potential primary angles to θ₁, θ₂, . . . , θ_(M) and construct anangle dictionary 606 for this list of angles:

A=[a(θ₁),a(θ₂), . . . ,a(θ_(M))]  (2)

Each column of the angle dictionary 606 is the steering vector for oneangle.

At 608, the angle-finding module 116 determines, using anL1-minimization-based function and the auxiliary EM energy 408, non-zeroelements in a selection vector. The non-zero elements in the selectionvector represent the object angles of the angle dictionary 606 thatcorrespond to the angles of the respective objects 120. Theangle-finding module 116 can use the following equation to identify theangles:

y=Ax+η  (3)

where the K×1 vector y represents the measured beam vector of theauxiliary EM energy 408 received by the dense ULA 206, the vector xrepresents a sparse vector, and the vector η represents measurementnoise. The angle-finding module 116 considers x as the selection vector.The steering vectors in A corresponding to the non-zero elements in xrepresent the actual angles.

The angle-finding module 116 can solve for the selection vector x inEquation (3) by solving the following L1-minimization:

$\begin{matrix}{{\hat{x} = {\arg\min\limits_{x}{x}_{1}}},{{s.t.{{y - {Ax}}}_{2}} \leq \varepsilon}} & (4)\end{matrix}$

where ε bounds the amount of noise in the data. The angle-finding module116 can solve Equation (4) using, for example, an Orthogonal MatchingPursuit (OMP) based-function.

Example Method

FIG. 7 illustrates a flow diagram of an example method 700 of the radarsystem 102 with a sparse linear array and a dense auxiliary lineararray. Method 700 is shown as sets of operations (or acts) performed,but not necessarily limited to the order or combinations in which theoperations are shown herein. Further, any of one or more of theoperations may be repeated, combined, or reorganized to provide othermethods. In portions of the following discussion, reference may be madeto the environment 100 of FIG. 1 , and entities detailed in FIGS. 1through 6 , reference to which is made for example only. The techniquesare not limited to performance by one entity or multiple entities.

At 702, one or more processors of a radar system determines, based on EMenergy that is received at a primary subarray of an antenna array, firstpotential angles of one or more objects that are reflecting the EMenergy to the antenna array. The primary subarray includes multiplefirst antenna elements. For example, the sparse ULA 204 of the antenna110 receives EM energy reflected by one or more objects 120. Theprocessor 112 of the radar system 102 determines, based on the primaryEM energy 402 received by the sparse ULA 204, potential primary angles406 of the one or more objects 120. The sparse ULA 204 includes Mantenna elements 208.

At 704, the processor of the radar system determines, based on EM energythat is received at an auxiliary subarray of the antenna array, secondpotential angles of the one or more objects that are reflecting the EMenergy to the antenna array. The auxiliary subarray includes multiplesecond antenna elements. The second antenna elements have a smallerspacing than the first antenna elements. For example, the dense ULA 206of the antenna 110 receives EM energy reflected by the one or moreobjects 120. The processor 112 determines, based on the auxiliary EMenergy 408 received by the dense ULA 206, potential auxiliary angles 412of the one or more objects 120. The dense ULA 206 includes N antennaelements 208, which have a smaller dense spacing d_(D) 212 than thesparse spacing d_(S) 210 for the antenna elements 208 of the sparse ULA204.

At 706, the processor of the radar system determines, based on the firstpotential angles and the second potential angles, at least onerespective angle associated with each of the one or more objects. Forexample, the processor 112 determines, based on the potential primaryangles 406 and the potential auxiliary angles 412, at least onerespective angle associated with each of the one or more objects 120.The resolution of the potential primary angles 406 and the potentialauxiliary angles 412 to determine the respective object angle(s) isdescribed in greater detail above with respect to FIGS. 4 through 6 .

Examples

In the following section, examples are provided.

Example 1: A radar system comprising one or more processors configuredto: determine, based on electromagnetic (EM) energy that is received ata primary subarray of an antenna array, first potential angles of one ormore objects that are reflecting the EM energy to the antenna array, theprimary subarray comprising multiple first antenna elements; determine,based on the EM energy that is received at an auxiliary subarray of theantenna array, second potential angles of the one or more objects, theauxiliary subarray comprising multiple second antenna elements, thesecond antenna elements having a smaller spacing than the first antennaelements; and determine, based on the first potential angles and thesecond potential angles, at least one respective angle associated witheach of the one or more objects.

Example 2: The radar system of example 1, wherein in determining the atleast one respective angle associated with each of the one or moreobjects, the one or more processors are configured to: generate, basedon the EM energy that is respectively received at the primary subarrayand the auxiliary subarray, fast Fourier transform (FFT) spectrummagnitudes for the primary subarray and the auxiliary subarray using anFFT with a pre-defined window; normalize and align the FFT spectrummagnitudes for the primary subarray and the auxiliary subarray;identify, based on the normalized and aligned FFT spectrum magnitudes,primary spectrum peaks and auxiliary spectrum peaks; filter out, basedon at least one of a magnitude or slope, unqualified spectrum peaks fromamong the primary spectrum peaks and the auxiliary spectrum peaks; andoutput non-filtered spectrum peaks from among the primary spectrum peaksand the auxiliary spectrum peaks as the at least one respective angleassociated with each of the one or more objects.

Example 3: The radar system of example 2, wherein the primary spectrumpeaks and auxiliary spectrum peaks are identified as peaks from thenormalized and aligned FFT spectrum magnitudes that are above athreshold value.

Example 4: The radar system of example 3, wherein the threshold value isinversely proportional to a signal-to-noise ratio of the EM energyreceived at the auxiliary subarray.

Example 5: The radar system of example 2, wherein in determining the atleast one respective angle associated with each of the one or moreobjects, the one or more processors are further configured to: generatean angle dictionary by unfolding the first potential angles; filter theunfolded first potential angles from the FFT spectrum magnitudes for theauxiliary subarray to construct an angle dictionary; and determine,using an L1-minimization-based function and the EM energy that isreceived at the auxiliary subarray, non-zero elements in a selectionvector, the non-zero elements in the selection vector representing theat least one respective angle associated with each of the one or moreobjects.

Example 6: The radar system of example 1, wherein the primary subarrayand the auxiliary subarray are uniform linear arrays, wherein theantenna elements of the uniform linear arrays are equally spaced.

Example 7: The radar system of example 1, wherein the primary subarrayis positioned in an azimuth direction, and the auxiliary subarray ispositioned in line with the primary subarray in the same azimuthdirection.

Example 8: The radar system of example 1, wherein the primary subarrayand the auxiliary subarray are positioned in an azimuth direction, andthe auxiliary subarray is positioned with an elevation offset from theprimary subarray.

Example 9: The radar system of example 1, wherein the primary subarrayand the auxiliary subarray are positioned in an azimuth direction, andthe auxiliary subarray overlaps with at least a portion of the primarysubarray.

Example 10: The radar system of example 1, wherein a quantity of thefirst antenna elements is greater than a quantity of the second antennaelements.

Example 11: The radar system of example 1, wherein a ratio of a spacingof the first antenna elements to a spacing of the second antennaelements is approximately equal to an integer.

Example 12: The radar system of example 11, wherein the integer is anexponential of two.

Example 13: The radar system of example 1, wherein the radar system isconfigured to be installed on an automobile.

Example 14: A method comprising: determining, based on electromagnetic(EM) energy that is received at a primary subarray of an antenna array,first potential angles of one or more objects that are reflecting the EMenergy to the antenna array, the primary subarray comprising multiplefirst antenna elements; determining, based on the EM energy that isreceived at an auxiliary subarray of the antenna array, second potentialangles of the one or more objects, the auxiliary subarray comprisingmultiple second antenna elements, the second antenna elements having asmaller spacing than the first antenna elements; and determining, basedon the first potential angles and the second potential angles, at leastone respective angle associated with each of the one or more objects.

Example 15: The method of example 14, wherein determining the at leastone respective angle associated with each of the one or more objectscomprises: generating, based on the EM energy that is respectivelyreceived at the primary subarray and the auxiliary subarray, fastFourier transform (FFT) spectrum magnitudes for the primary subarray andthe auxiliary subarray using an FFT with a pre-defined window;normalizing and aligning the FFT spectrum magnitudes for the primarysubarray and the auxiliary subarray; identifying, based on thenormalized and aligned FFT spectrum magnitudes, primary spectrum peaksand auxiliary spectrum peaks; filtering out, based on at least one of amagnitude or slope, unqualified spectrum peaks from among the primaryspectrum peaks and the auxiliary spectrum peaks; and outputtingnon-filtered spectrum peaks from among the primary spectrum peaks andthe auxiliary spectrum peaks as the at least one respective angleassociated with each of the one or more objects.

Example 16: The method of example 15, wherein the primary spectrum peaksand auxiliary spectrum peaks are identified as peaks from the normalizedand aligned FFT spectrum magnitudes that are above a threshold value.

Example 17: The method of example 16, wherein the threshold value isinversely proportional to a signal-to-noise ratio of the EM energyreceived at the auxiliary subarray.

Example 18: The method of example 15, wherein determining the at leastone respective angle associated with each of the one or more objectsfurther comprises: generating an angle dictionary by unfolding the firstpotential angles; filtering the unfolded first potential angles from theFFT spectrum magnitudes for the auxiliary subarray to construct an angledictionary; and determining, using an L1-minimization-based function andthe EM energy that is received at the auxiliary subarray, non-zeroelements in a selection vector, the non-zero elements in the selectionvector representing the at least one respective angle associated witheach of the one or more objects.

Example 19: A computer-readable storage media comprisingcomputer-executable instructions that, when executed, cause a processorof a radar system to: determine, based on electromagnetic (EM) energythat is received at a primary subarray of an antenna array, firstpotential angles of one or more objects that are reflecting the EMenergy to the antenna array, the primary subarray comprising multiplefirst antenna elements; determine, based on the EM energy that isreceived at an auxiliary subarray of the antenna array, second potentialangles of the one or more objects, the auxiliary subarray comprisingmultiple second antenna elements, the second antenna elements having asmaller spacing than the first antenna elements; and determine, based onthe first potential angles and the second potential angles, at least onerespective angle associated with each of the one or more objects.

Example 20: The computer-readable storage media of example 19, whereinthe instructions, when executed, cause the processor of the radar systemto determine the at least one respective angle associated with each ofthe one or more objects by: generating, based on the EM energy that isrespectively received at the primary subarray and the auxiliarysubarray, fast Fourier transform (FFT) spectrum magnitudes for theprimary subarray and the auxiliary subarray using an FFT with apre-defined window; normalizing and aligning the FFT spectrum magnitudesfor the primary subarray and the auxiliary subarray; identifying, basedon the normalized and aligned FFT spectrum magnitudes, primary spectrumpeaks and auxiliary spectrum peaks; filtering out, based on at least oneof a magnitude or slope, unqualified spectrum peaks from among theprimary spectrum peaks and the auxiliary spectrum peaks; and outputtingnon-filtered spectrum peaks from among the primary spectrum peaks andthe auxiliary spectrum peaks as the at least one respective angleassociated with each of the one or more objects.

CONCLUSION

While various embodiments of the disclosure are described in theforegoing description and shown in the drawings, it is to be understoodthat this disclosure is not limited thereto but may be variouslyembodied to practice within the scope of the following claims. From theforegoing description, it will be apparent that various changes may bemade without departing from the spirit and scope of the disclosure asdefined by the following claims.

What is claimed is:
 1. A radar system comprising one or more processorsconfigured to: determine, based on electromagnetic (EM) energy that isreceived at a first subarray of an antenna array, first potential anglesof one or more objects that are reflecting the EM energy to the antennaarray, the first subarray comprising multiple first antenna elements;determine, based on the EM energy that is received at a second subarrayof the antenna array, second potential angles of the one or moreobjects, the second subarray comprising multiple second antennaelements, the second antenna elements having a smaller spacing than thefirst antenna elements, a ratio of a spacing of the first antennaelements to a spacing of the second antenna elements being equal to aninteger, the integer being equal to an exponential of two and greaterthan two; and determine, based on the first potential angles and thesecond potential angles, a respective angle associated with each of theone or more objects.
 2. The radar system of claim 1, wherein the firstsubarray and the second subarray are uniform linear arrays.
 3. The radarsystem of claim 1, wherein the first subarray is positioned in anazimuth direction and the second subarray is positioned in line with thefirst subarray in the azimuth direction but offset along an elevationdirection.
 4. The radar system of claim 1, wherein the first subarray ispositioned in an elevation direction and the second subarray ispositioned in line with the first subarray in the elevation directionbut offset along an azimuth direction.
 5. The radar system of claim 1,wherein the first subarray and the second subarray are positioned in anelevation direction, and the second subarray overlaps with at least aportion of the first subarray.
 6. The radar system of claim 1, wherein:the first subarray comprises a first two-dimensional (2D) array with themultiple first antenna elements positioned in an azimuth direction andan elevation direction; the first potential angles comprise firstpotential azimuth angles and first potential elevation angles; thesecond subarray comprises a second 2D array with the multiple secondantenna elements positioned in the azimuth direction and the elevationdirection; the second potential angles comprise second potential azimuthangles and second potential elevation angles; a first ratio of anazimuth spacing of the first antenna elements in the azimuth directionto an azimuth spacing of the second antenna elements in the azimuthdirection is equal to a first integer, the first integer is equal to anexponential of two and greater than two; a second ratio of an elevationspacing of the first antenna elements in the elevation direction to anelevation spacing of the second antenna elements in the elevationdirection is equal to a second integer, the second integer is equal toan exponential of two and greater than two; and the angle comprises anazimuth angle and an elevation angle associated with each of the one ormore objects.
 7. The radar system of claim 6, wherein the first 2D arrayoverlaps the second 2D array.
 8. The radar system of claim 6, whereinthe first 2D array is offset in the azimuth direction or elevationdirection from the second 2D array.
 9. The radar system of claim 1,wherein a field-of-view of the second subarray is based on the spacingof the second antenna elements.
 10. Computer-readable storage mediacomprising computer-executable instructions that, when executed, cause aprocessor of a radar system to: determine, based on electromagnetic (EM)energy that is received at a first subarray of an antenna array, firstpotential angles of one or more objects that are reflecting the EMenergy to the antenna array, the first subarray comprising multiplefirst antenna elements; determine, based on the EM energy that isreceived at a second subarray of the antenna array, second potentialangles of the one or more objects, the second subarray comprisingmultiple second antenna elements, the second antenna elements having asmaller spacing than the first antenna elements, a ratio of a spacing ofthe first antenna elements to a spacing of the second antenna elementsbeing equal to an integer, the integer being equal to an exponential oftwo and greater than two; and determine, based on the first potentialangles and the second potential angles, a respective angle associatedwith each of the one or more objects.
 11. The computer-readable storagemedia of claim 10, wherein the first subarray and the second subarrayare uniform linear arrays.
 12. The computer-readable storage media ofclaim 10, wherein the first subarray is positioned in an azimuthdirection and the second subarray is positioned in line with the firstsubarray in the azimuth direction but offset along an elevationdirection.
 13. The computer-readable storage media of claim 10, whereinthe first subarray is positioned in an elevation direction and thesecond subarray is positioned in line with the first subarray in theelevation direction but offset along an azimuth direction.
 14. Thecomputer-readable storage media of claim 10, wherein the first subarrayand the second subarray are positioned in an elevation direction, andthe second subarray overlaps with at least a portion of the firstsubarray.
 15. The computer-readable storage media of claim 10, wherein:the first subarray comprises a first two-dimensional (2D) array with themultiple first antenna elements positioned in an azimuth direction andan elevation direction; the first potential angles comprise firstpotential azimuth angles and first potential elevation angles; thesecond subarray comprises a second 2D array with the multiple secondantenna elements positioned in the azimuth direction and the elevationdirection; the second potential angles comprise second potential azimuthangles and second potential elevation angles; a first ratio of anazimuth spacing of the first antenna elements in the azimuth directionto an azimuth spacing of the second antenna elements in the azimuthdirection is equal to a first integer, the first integer is equal to anexponential of two and greater than two; a second ratio of an elevationspacing of the first antenna elements in the elevation direction to anelevation spacing of the second antenna elements in the elevationdirection is equal to a second integer, the second integer is equal toan exponential of two and greater than two; and the angle comprises anazimuth angle and an elevation angle associated with each of the one ormore objects.
 16. The computer-readable storage media of claim 15,wherein the first 2D array overlaps the second 2D array.
 17. Thecomputer-readable storage media of claim 15, wherein the first 2D arrayis offset in the azimuth direction or elevation direction from thesecond 2D array.
 18. The computer-readable storage media of claim 10,wherein a field-of-view of the second subarray is based on the spacingof the second antenna elements.
 19. A method comprising: determining,based on electromagnetic (EM) energy that is received at a firstsubarray of an antenna array, first potential angles of one or moreobjects that are reflecting the EM energy to the antenna array, thefirst subarray comprising multiple first antenna elements; determining,based on the EM energy that is received at a second subarray of theantenna array, second potential angles of the one or more objects, thesecond subarray comprising multiple second antenna elements, the secondantenna elements having a smaller spacing than the first antennaelements, a ratio of a spacing of the first antenna elements to aspacing of the second antenna elements being equal to an integer, theinteger being equal to an exponential of two and greater than two; anddetermining, based on the first potential angles and the secondpotential angles, a respective angle associated with each of the one ormore objects.
 20. The method of claim 19, wherein: the first subarraycomprises a first two-dimensional (2D) array with the multiple firstantenna elements positioned in an azimuth direction and an elevationdirection; the first potential angles comprise first potential azimuthangles and first potential elevation angles; the second subarraycomprises a second 2D array with the multiple second antenna elementspositioned in the azimuth direction and the elevation direction; thesecond potential angles comprise second potential azimuth angles andsecond potential elevation angles; a first ratio of an azimuth spacingof the first antenna elements in the azimuth direction to an azimuthspacing of the second antenna elements in the azimuth direction is equalto a first integer, the first integer is equal to an exponential of twoand greater than two; a second ratio of an elevation spacing of thefirst antenna elements in the elevation direction to an elevationspacing of the second antenna elements in the elevation direction isequal to a second integer, the second integer is equal to an exponentialof two and greater than two; and the angle comprises an azimuth angleand an elevation angle associated with each of the one or more objects.